00:01
So for this problem, we are given the setup that is shown in the speaker.
00:06
We have a mass capital m that rests on a frictionless surface, and it is also connected to an horizontal screen with a constant k, and to the other end is attached to the wall.
00:24
Now there is a second block with mass lower case m that rests on top of of this first block.
00:32
Now the coefficient of static friction between the block between these two blocks is also given and what we need to find is the maximum amplitude of the oscillation such that the top block, the block with the mass lower km and we will not sleep on the bottom of the other block.
00:59
Now, in order to do that, we know that the maximum acceleration that these systems can have is equal to the spring constants times the amplitude, the one that we want to calculate, times the total mass of this system.
01:27
And what we need to do is to apply newton's law to the, the mass at the top.
01:35
Now, the maximum acceleration of the lower block can exceed the maximum acceleration that can be given to the outer block by the frictional force.
01:46
So it can exceed that value that we just put in here.
01:50
Now, for the block m at the top, the maximum frictional force that this can be inserted on it, we know before it starts to move, is equal to the product between the the coefficient of static friction times the normal force.
02:18
Now in this case, the normal force is the same as the weight, because the normal is always perpendicular to the surface, and the weight is always pointing towards the center of the earth.
02:32
So in this case, we have that the normal force is just equal to the weight, so we will have that that is the mass of this blood, times the acceleration due to gravity times the coefficient.
02:43
That is the static frictional force, the maximum.
02:47
Now, applying newton's second's law, we obtain that this frictional force, the only one that is experienced the block at the top, is going to be the frictional force is going to be equal to the mass of this times the acceleration...
